Fact- yes in a lab, a section of the weld could be dated depending on what was used to weld it. 14-C has a specific half-life, or decay rate that would be used in the calculation.
Opinion- I think the factory worker repaired something (in your story), but I do not know how stringent quality control was (in your storyline)
Fact- Times were lean and resources were valuable and scarce (assuming you mean this factory worker was in an auto factory WWII-Korean Era). Things were repaired.
Edit- if this "can you carbon date a weld" is informational, fine, but I wanted to let you know that mass spectrometry labs are phenomenally expensive. Just in case your next question went there.
Brad
